mlsanityData to 7 Oct 2026

Convergence of the Deep BSDE Method for Coupled FBSDEs

arXiv 1811.01165 ↗First posted 3 Nov 2018math.PR cs.LG cs.NAcited by 42

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Abstract (arXiv)

The recently proposed numerical algorithm, deep BSDE method, has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). This article lays a theoretical foundation for the deep BSDE method in the general case of coupled FBSDEs. In particular, a posteriori error estimation of the solution is provided and it is proved that the error converges to zero given the universal approximation capability of neural networks. Numerical results are presented to demonstrate the accuracy of the analyzed algorithm in solving high-dimensional coupled FBSDEs.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Nov 2018.

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Citing papers per year: 2021: 6; 2022: 7; 2023: 6; 2024: 8; 2025: 10; 2026: 5.

42 papers.

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  1. 2021Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problemscited by 21
  2. 2021Deep Learning for Mean Field Games and Mean Field Control with Applications to Financecited by 20
  3. 2021Reproducing Activation Function for Deep Learningcited by 19
  4. 2022Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependencecited by 13
  5. 2021Solving PDEs on Unknown Manifolds with Machine Learningcited by 12
  6. 2024Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEscited by 12
  7. 2022Convergence of a robust deep FBSDE method for stochastic controlcited by 11
  8. 2022Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learningcited by 9
  9. 2022Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problemscited by 9
  10. 2022Deep Signature Algorithm for Multi-dimensional Path-Dependent Optionscited by 6
  11. 2023Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumpscited by 6
  12. 2021Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematicscited by 5
30 more
  1. 2022Approximating Discontinuous Nash Equilibrial Values of Two-Player General-Sum Differential Gamescited by 5
  2. 2023Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generationcited by 5
  3. 2023From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEscited by 5
  4. 2025A brief review of the Deep BSDE method for solving high-dimensional partial differential equationscited by 5
  5. 2024A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equationscited by 4
  6. 2024FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equationscited by 4
  7. 2023Value Approximation for Two-Player General-Sum Differential Games with State Constraintscited by 3
  8. 2024Pontryagin Neural Operator for Solving Parametric General-Sum Differential Gamescited by 3
  9. 2024Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in Lp-sensecited by 3
  10. 2025Integration Matters for Learning PDEs with Backward SDEscited by 3
  11. 2022A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEscited by 2
  12. 2025Continuous-Time Value Iteration for Multi-Agent Reinforcement Learningcited by 2
  13. 2021A novel control method for solving high-dimensional Hamiltonian systems through deep neural networkscited by 1
  14. 2023Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equationscited by 1
  15. 2025A deep solver for backward stochastic Volterra integral equationscited by 1
  16. 2025Nonlinear filtering based on density approximation and deep BSDE predictioncited by 1
  17. 2026Learn and Verify: A Framework for Rigorous Verification of Physics-Informed Neural Networkscited by 1
  18. 2023Deep Generative Modeling with Backward Stochastic Differential Equationscited by 0
  19. 2024A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agentscited by 0
  20. 2024A forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equationscited by 0
  21. 2024Deep Operator BSDE: a Numerical Scheme to Approximate Solution Operatorscited by 0
  22. 2025Generative Market Equilibrium Models with Stable Adversarial Learning via Reinforcementcited by 0
  23. 2025A Reverse-BSDE Diffusion Samplercited by 0
  24. 2025Error analysis for the deep Kolmogorov methodcited by 0
  25. 2025High-dimensional Bayesian filtering through deep density approximationcited by 0
  26. 2025A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applicationscited by 0
  27. 2026A Schr"odinger Eigenfunction Method for Long-Horizon Stochastic Optimal Controlcited by 0
  28. 2026A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent L'evy Jumpscited by 0
  29. 2026A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatchcited by 0
  30. 2026Deep Learning for Reflected BSDEs: Regularization and Error Analysiscited by 0